20%??

[pete fabrizio]

Sagah has suggested in multiple posts now that a PLO player would optimally play around 20% of hands. I find this hard to believe. Personally, I have been known to play upwards of 40-45% of hands when I'm a monster stack trying to run over the table, and I play around 35% on average. Now, I shouldn't be used as an example, since I DEFINITELY play "too many" hands, but what I've found is that there's not THAT much room to trim: Even when I've tried playing super-tight, I can't get my %age much below 30.

Could any of you tell me what that 10% range that I'm playing (even when I'm playing super-tight) that I shouldn't be playing actually is?

Sag, could you give me examples of some specific hands that you suspect I am playing unprofitably? (aside from 778J)

[sahaguje]

Hi,

I usually play 20% of my hands in tough games online when I first sit. It would be different in live games, where I can buy in for more than 100 BB, giving me better implied odds, or when I doubled up so I have 200, or also when the game is passive and often unraised preflop.
I am not a big fan of maths, but let's give an intuitive shot. Let's say the game is ten handed, so 10% of the time I have the best hand preflop. If the pot is always played heads up between the best and the second best hand, and if all the players have the same level, then I should only play those 10% best hands, then I will be a favorite everytime I play. Now if the hand is played between the three best hands (30% of hands dealt), if I play my 15% best hands, I should maximize my EV. And if 40% of hands are played preflop (average in tough games), playing the 20% best should be optimum. But I dont know at all if it makes any sense...

Let me give another reason : most NLHE experts advocate playing 15-20 of your hands. I think this percentage is not very game-dependant, it should be an intuitive approximation of a mathematical rule from game theory, considering the optimum number of hands you should play when 10 players are dealt random hands that can roughly be classified. I cant explain why exaclty, but I am quite sure the optimum percentage of hands play dont depend on the game played, but on the structure, the stackes, and the looseness of the games. So I play as many hands in every game of similar structure, whether it is stud, HE, Omaha, Omaha 8 etc.

A last reason : I think a good player should always play less hands than the other players at the table. Once again, I am sure game theory could help me understand why, but I havent studied it. Usually, when a friend asks me how many hands he should play preflop, I advise him to play between 20 and 10% less than the oither players, depemding on his level. Since I want to minimize my swings, and I consider myself a poor PLO player, I want to play about 20% less hands than the other players in a tough PLO game.

Considering hand selection, it is very position and game dependant. I prefer playing only the best hands (if I play 20% statistically I play mostly first and second hands dealt), and play them for a raise if I have position. But if you give me precise examples of hands, I can telle you if I play them or not.

Sorry, this post is confused, and I use concepts I dont like (at PLO, tougher to classify hands as easily as at NLHE). But I think it is a very intersting question. If experts could give their answers...

[pete fabrizio]

This post was fraught with logical errors. In fact, your three main reasons for playing 20% of hands are all dead wrong

1.
[ QUOTE ]
I am not a big fan of maths, but let's give an intuitive shot. Let's say the game is ten handed, so 10% of the time I have the best hand preflop. If the pot is always played heads up between the best and the second best hand, and if all the players have the same level, then I should only play those 10% best hands, then I will be a favorite everytime I play. Now if the hand is played between the three best hands (30% of hands dealt), if I play my 15% best hands, I should maximize my EV. And if 40% of hands are played preflop (average in tough games), playing the 20% best should be optimum. But I dont know at all if it makes any sense...

[/ QUOTE ]

This little thought-experiment is deeply misguided. The notion that you can guarantee e.v. merely by cutting the “losing” 20% of hands is ridiculous. Imagine for one second that the table contains 10 clones of yourself, and you play perfectly. On average, you play 30% of hands. Do you think one of your clones could actually improve his E.V. by decided to play only 15% of hands? What hands would he be cutting? Well, by the stipulation that you play perfectly, he would be dumping only profitable situations. Thus, the clone who only played 15% of his hands would be the fish! He would be failing to extract equity when it exists! Suddenly everyone at the table would have a + E.V. except for him.

And just to make an obvious point, let’s say that clone actually could make money by playing half as many hands as you. What would the game-theoretical response to that be? Well, the other clones should start playing 7.5%, 3.75%, and so on, until all clones play 0 hands, and you can just go home.

Certainly you can make money in poker by playing fewer hands than your opponents, but not inherently, as you wrongly suggest. You make money by recognizing situations that aren’t profitable and avoiding them - the same situations that your opponents gladly enter.

2.
[ QUOTE ]
Let me give another reason : most NLHE experts advocate playing 15-20 of your hands. I think this percentage is not very game-dependant, it should be an intuitive approximation of a mathematical rule from game theory, considering the optimum number of hands you should play when 10 players are dealt random hands that can roughly be classified. I cant explain why exaclty, but I am quite sure the optimum percentage of hands play dont depend on the game played, but on the structure, the stackes, and the looseness of the games. So I play as many hands in every game of similar structure, whether it is stud, HE, Omaha, Omaha 8 etc.

[/ QUOTE ]

This is also just game-theoretically incorrect. The optimum percentage of hands played absolutely depends on the game you are playing -- specifically, it depends on the variance involved in that game, your likelihood of catching up after the flop, and the likelihood of an individual hand ending up the winner against the field. In hold-em, the optimal number of hands that you should play is fairly low because it is hard to “catch up” with the winning hand. The first limitation on how many PLO hands is optimal should be the instant recognition that it should be higher.

If you don’t see the relationship between variance and %age of hands played, imagine a game in which a hand could be no more than a 1% favorite against 80% of hands, but would be a 90% favorite against the other 20%. Blinds are $10 and your stack is $100. You are playing 3-handed and someone raises all-in UTG -- What %age of hands should you be calling with? Clearly you should call with all hands that are in the 80% category, and fold the other 20%. You would make money in this game from times when people call with the 20%, or times when people fold the 80%, or when someone tries to bluff you with the 20%, etc -- but you would be playing a LOT of hands in this game.

3.
[ QUOTE ]
A last reason : I think a good player should always play less hands than the other players at the table. Once again, I am sure game theory could help me understand why, but I havent studied it. Usually, when a friend asks me how many hands he should play preflop, I advise him to play between 20 and 10% less than the oither players, depemding on his level. Since I want to minimize my swings, and I consider myself a poor PLO player, I want to play about 20% less hands than the other players in a tough PLO game.


[/ QUOTE ]

I think it is generally the case that a good player will end up playing less hands than average at any table -- even I play a bit less than average. However, it by no means follows that they should “game theoretically.” If, god help me, I’m playing at a rock table where everyone is passing up profitable situations, I would be remiss to pass up even MORE profitable situations myself. In that case, I should definitely be playing MORE hands than everyone else. You should only be playing 10% less than the other players if, by your estimation, the other players are playing 10% too many hands. Again, your fundamental error here is that you seem to think that throwing away perfectly good hands somehow gives you an inherent “game theoretical” edge. As someone who has dabbled in both game theory and logic, I can tell you that your thoughts here run afoul of both.

[Zag]

I agree with Pete, here, on his comments about game theory. There is a percentage which is the theoretical best percentage against an unknown opponent who is as likely to play too loose as too tight. If all players are playing at this percentage (and they all play equally well postflop) then for one to deviate from this percentage in either direction would be detrimental. (I don't know what that percentage is, exactly, but it is certainly somewhere between 10% and 25%.)

That said, the vast majority of players play too loosely. Given that assumption, the most common case is that you want to be tighter than the others at your table.

I also suspect that the correct percentage of hands that you should play is slightly higher for Omaha than for Hold'em. This is because there is less of an overlay, preflop, of the best hands vs. the worst hands. In Hold'em, you can have a preflop domination of 14-to-1 of As Ah over Ac 6s, for instance. In O8, the most significant level of domination I have found (in 3 tries) is 4-to-1 (Ah As 2h 3s vs. Ac 3d 8h Ks).

I have spent more hours than I care to admit dealing out Omaha hands, hoping to get a feel for the game. Try this: Deal out 6 Omaha hands, and pick the two that you think are best, but leave them all visible. Now deal out 25 of the remaining 28 cards into a 5 by 5 square, so that they represent 10 different boards, 5 rows and 5 columns. Now evaluate all 10 boards for the original 6 hands, giving 1 point to a hand when it wins half a pot, and 3 points for a scoop. Did the two hands that you selected originally finish first and second? I find that they usually don't, not because I selected poorly, but because there is a lot of luck involved.

I have found that the predicted winners in hold'em are the big point winners most of the time.

Note that, if you do the same experiment, but instead you deal the flop before choosing your two winners, and then you deal out 12 different turn & river groups, pretty much the "best" hands will be the winners at the end. In other words, the flop defines the hands pretty well, even when they are not that well defined preflop.

If anyone hasn't played games with himself like this, I highly recommend it. I have found that it really helps with getting the feel of a game.

[Paul2432]

The biggest domination in Omaha occurs when two hands hold the same ranks but one is double suited and the other holds four different suits. The double suited hand cannot lose.

That sounds like an interesting excersize. I will have to try it.

Paul

[pete fabrizio]

Um, that is hardly the biggest domination. The biggest domination is 33xx vs. 2222, where the 33xx will ALWAYS scoop.

[Zag]

[ QUOTE ]
The biggest domination in Omaha occurs when two hands hold the same ranks but one is double suited and the other holds four different suits. The double suited hand cannot lose.

Paul

[/ QUOTE ]

Actually, this is not that much of an edge, because you end up chopping most of the time, even though you are correct that you never, ever lose. Twodimes puts it at 0.549-to-0.451, or 1.22-to-1. I would still prefer the Hold'em matchup of AA vs. A2.

Pete's response is, of course, correct, but I was trying to limit it to somewhat realistic hands. (OK, I just didn't think of it.)

[Big Dave D]

I also thought the 20% was crazy.

I don't want to keep on pluggin my site...ok I do [img]/images/graemlins/smile.gif[/img]...but I did talk about this. Currently the PLO 5-10 is at the 3rd stage. Maybe the games sahaguje play are at stage 1. It does make a hell of a difference.

Another self-aggrandizing link [img]/images/graemlins/smile.gif[/img]

gl

dd

[sahaguje]

OK, after a good sleep night, I think I was right, and I am going to defend my position...

Let s redefine it : in each game, considering your position, the stacks and the level of other players, you can define an optimal number of hands to play. This number is closely related to two things :
- The numer of players in the game, because it defines your probability to have the first, second, third etc. best hand.
- The distribution of probabilities of winning among the hands : The best hand has a probability of p(1), to win, the second hand p(2) etc, in each poker game, but p(i)-p(i-1) is different in every form of poker.

In a future post, I am gonna try to prove this mathematically. Here I just want to explain why I think this is theoretically right to play only a certain proportion of hands, and this proportion is linked with the distribution of probabilities of winning the hands between players. First I will answer to pete's post, "fraught with logical errors"

[ QUOTE ]

This little thought-experiment is deeply misguided. The notion that you can guarantee e.v. merely by cutting the “losing” 20% of hands is ridiculous. Imagine for one second that the table contains 10 clones of yourself, and you play perfectly. On average, you play 30% of hands. Do you think one of your clones could actually improve his E.V. by decided to play only 15% of hands? What hands would he be cutting? Well, by the stipulation that you play perfectly, he would be dumping only profitable situations. Thus, the clone who only played 15% of his hands would be the fish! He would be failing to extract equity when it exists! Suddenly everyone at the table would have a + E.V. except for him.

And just to make an obvious point, let’s say that clone actually could make money by playing half as many hands as you. What would the game-theoretical response to that be? Well, the other clones should start playing 7.5%, 3.75%, and so on, until all clones play 0 hands, and you can just go home.

[/ QUOTE ]

Thanks for giving me such an example. The problem in what you say is that you dont consider the other clones' hands, but only mines. It is faulty to say that if I miss occasions to make +EV play, that means I am gonna be a fish. If there were no blinds, I could wait for AA ds and only play them, this would not be the most profitable play, but that does not mean at all I would have become a fish, and people now all win money just because I am more selective...

Anyway, if the table is full of clones (so no one is a better player), and if we consider there is no dead money in the pot, then when the pot is 4-handed, in the long run my probability of winning the hand has to be more than 25%, or else I would lose money. Remember I cannot make more money than the other players can when I have a hand, since we are all clones. But my probability to win the pot postflop when we are 4 is of course related with my probability to win the pot preflop when there are ten players, at least in the long run. The reason of this is obvious : in order to calculate the probability of a hand to win the pot, you must deal a great number of flops, and count each time this hand wins. That is what twodimes do, for example.

So, lets get back to the problem : each hand has p(i) chances to win the pot, i being the rank of the hand if we compare the probabilities ( ie : p(i-1)<p(i)<p(i+1) ). If the game is 10-handed, you should only play your p(1) hands, cause now you will be a favorite on every hand.

Notice two things : 1) that it is only true in the long run, and for a particular hand the p1 hand wont always be a favorite post flop. But if you play a great number of flops, it will be.
2) Since all players are clones, in the long run you cannot count on implied odds etc, because the other players will gain the same implied odds when they will be in your situation. So if we consider there is no dead money, 4 handed post flop, every hand that has more than 25% to win is a winner, and every hand that has less is a loser. Now you can tell there is money in the pot from preflop bets. That is true, and when I will calculate the "good" proportion of hands to play, I will try to take it into account, but here I just want to explain my point theoretically.

So you want to play your p1 hands only if you want to be a favorite each hand you play, or any hand that has more than 25% odds to win the pot if you want to take every opportunity to make a +EV play. Now sometimes, only 1 hand will have for than 1 to 3 odds, sometimes 3, but most of the times two hands will have odds sufficient enough, and 2 wont. If everybody does good hand selection, only p1, p2, p3 and p4 hands will be played each time ; so in the long run, p1 and p2 hands will show a profit, and p3 and p4 hands will lose money. So do maximize your winnings, you should only play 20% of your hands, if it is 4 handed post flop on average.

It is the same for every number of players : if it is 6 handed, you have to get 1-to-5 odds preflop to show a profit. In the long run, 3 hands will have more than these odds postflop, and in the long run again, it will be p1, p2 and p3 hands, so you should play 30% of your hands. etc etc etc.
That is what I meant when I said you should play half hands the other does ; I should have said you should play half the number of players in the pot, but of course it is the same thing. Now maybe it will not seem intuitive multiway, but it is obvious heads up : if there was no dead money and if you had the same level than your opponents, obviously the best strategy is to play only the hands that beat him, ie that has more than 50% odds to win the pot.

Now you see that all we said was true for every form of game. But since there are the blinds, and players bet money preflop, you are not forced to have more than 25% odds to win the pot if it is 4 handed post flop to make money, even if all the players are equal. It depends on the average pot size, and it can be easily calculated, I ll do that in a next post. So for example we can imagine if it is 4 handed post flop on average, you just have to have 20% (and not 25%) odds to win to make it profitable. The type of game (HE, stud, Omaha) determines the distribution of probabilities to win, so it now affects how many hands are above the 20% line. For example, p(i)-p(i-1) is usally really superior at hold em than at omaha, so there is a good chance that in the long run more hands at omaha can have a probability to win superior to 20% post flop when 4 handed. So you should play more hands at omaha than at HE. But notice that it only comes from the fact that there is money in the pot when flop betting round begins. And I guess it wont make an enormous difference, but once again, it is easy to calculate, and I will try to do it.

So the good proportion of hands to play should theoretically be slighty superior (5-10% max, I guess) to half the average number of players per flop, all other conditions being equal.

Now pete made a good point : if everyone knows that, they should reduce the numer of hands they play until 0, and there will be no game. It is totally true. It is the same at NLHE : theoretically, if there was no dead money, everyone should wait for AA, as long as everyone else does it ; to put it differently, if 9 players only play AA, and one player plays AA and KK, if there is no dead money this player will be a big loser in the long run.

So why are there games ?
1) Well, in the games I know, there are some blinds to fight for.
2) Players dont make the proper adjustment.
3) Hands you evaluate as p1 are always playable if they really are the best hands. That is 10% of hands. But since you cannot know for sure which is the best hand, you will play more or less hands.
4) There is a virtuous circle : if 2 players enter the pot, you can play at least your 15% best hands, so the player after you can play his 20% best hands, etc. That is one of the reasons you can play more hands when you have position, i.e. more informations on the future conditions of the hand played.
5) Most players think they are on average able to make money when they win, more than the addition of all the money they lose when they lose their hands. Most of them are wrong, but this is that bad evaluation that makes them play. Otherwise, there will be no poker games.

I wont comment the rest of pete's post. It is interesting, but not appropriate. Every example in it supposes there is blind money, and/or that he is better than the other players. For example, he says he should not reduce the number of hands he plays when they are only rocks at the table, but on the contrary raise this number. Major mistake, cause he can play as many hands he wants, if the other players just play the best 10% of their hands, then pete will be an outdog everytime he is paid preflop. To make money, he has to steal the blinds, or play better than his opponents post flop. If in addition to playing only their best hands, the rocks play them heavily and with great agressivity, both pre and post flop, pete will lost incredible amounts of money very quickly.

I hope this post was interesting, and not too boring. I ll try to mathematically apply that toughts to omaha, but only if my reasonig is good, so I will wait a little for that. Please, comment and criticize what I wrote.

See you

sahaguje

[pete fabrizio]

The gross misunderstanding of simple poker theory in this post is surprising, coming from someone who posts so authoritatively ("How much?", "Where to Play", etc). I would explain why, exactly, but you've already shown a mysterious contempt for reason.

On the bright side, your bad logic may inadvertantly lead you to play well for a lot of games.

Just one tiny bit of guidance: Your dismissal of the blinds in your analysis is alarming. I'm sure you've heard this before, but all poker is fundamentally a struggle for the dead money that is in the pot (blind or otherwise). No-blind-no-ante games reduce quickly to the absurd, and have little to do with poker as we know it.